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Saddlepoint Approximations with Applications

Saddlepoint Approximations with Applications

£99.99

Part of Cambridge Series in Statistical and Probabilistic Mathematics

  • Date Published: August 2007
  • availability: Available
  • format: Hardback
  • isbn: 9780521872508

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  • Modern statistical methods use complex, sophisticated models that can lead to intractable computations. Saddlepoint approximations can be the answer. Written from the user's point of view, this book explains in clear language how such approximate probability computations are made, taking readers from the very beginnings to current applications. The core material is presented in chapters 1-6 at an elementary mathematical level. Chapters 7-9 then give a highly readable account of higher-order asymptotic inference. Later chapters address areas where saddlepoint methods have had substantial impact: multivariate testing, stochastic systems and applied probability, bootstrap implementation in the transform domain, and Bayesian computation and inference. No previous background in the area is required. Data examples from real applications demonstrate the practical value of the methods. Ideal for graduate students and researchers in statistics, biostatistics, electrical engineering, econometrics, and applied mathematics, this is both an entry-level text and a valuable reference.

    • An accessible, readable introduction that equips the reader to use the methods for real applications
    • Abundant examples, both numerical and theoretical, build and reinforce skills and understanding
    • Author is a major contributor to the field: this is, and will remain, the book on saddlepoint approximation
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    Reviews & endorsements

    'The prose is clear, conversational, and occasionally enlivened with wry humour. The overall impression is of great readability. The author has set out to make saddlepoint approximations more accessible to the reader, aiming to simplify and clarify the sometimes turgid literature, and has succeeded admirably.' Journal of Applied Statistics

    'Today this is perhaps the most powerful method used in statistical theory and practice. … This big book with its big coverage of a big topic is a big addition to the big Cambridge series.' Journal of the Royal Statistical Society

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    Product details

    • Date Published: August 2007
    • format: Hardback
    • isbn: 9780521872508
    • length: 578 pages
    • dimensions: 253 x 183 x 33 mm
    • weight: 1.21kg
    • contains: 131 b/w illus. 120 tables 283 exercises
    • availability: Available
  • Table of Contents

    Preface
    1. Fundamental approximations
    2. Properties and derivatives
    3. Multivariate densities
    4. Conditional densities and distribution functions
    5. Exponential families and tilted distributions
    6. Further exponential family examples and theory
    7. Probability computation with p*
    8. Probabilities with r*-type approximations
    9. Nuisance parameters
    10. Sequential saddlepoint applications
    11. Applications to multivariate testing
    12. Ratios and roots of estimating equations
    13. First passage and time to event distributions
    14. Bootstrapping in the transform domain
    15. Bayesian applications
    16. Non-normal bases
    References
    Index.

  • Author

    Ronald W. Butler, Southern Methodist University, Texas
    Ronald W. Butler is Professor of Statistics at Colorado State University. His statistical work on prediction, likelihood methods, and saddlepoint methods is widely known. His more recent work concerns the study of complex stochastic systems, reliability, and survival analysis, with applications to electrical engineering and medical statistics. In applied mathematics, he has made important contributions to the approximation of hypergeometric functions with matrix and vector arguments.

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